Probability Approximations And Beyond
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Probability Approximations And Beyond
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Author : Andrew Barbour
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-12-08
Probability Approximations And Beyond written by Andrew Barbour and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-08 with Mathematics categories.
In June 2010, a conference, Probability Approximations and Beyond, was held at the National University of Singapore (NUS), in honor of pioneering mathematician Louis Chen. Chen made the first of several seminal contributions to the theory and application of Stein’s method. One of his most important contributions has been to turn Stein’s concentration inequality idea into an effective tool for providing error bounds for the normal approximation in many settings, and in particular for sums of random variables exhibiting only local dependence. This conference attracted a large audience that came to pay homage to Chen and to hear presentations by colleagues who have worked with him in special ways over the past 40+ years. The papers in this volume attest to how Louis Chen’s cutting-edge ideas influenced and continue to influence such areas as molecular biology and computer science. He has developed applications of his work on Poisson approximation to problems of signal detection in computational biology. The original papers contained in this book provide historical context for Chen’s work alongside commentary on some of his major contributions by noteworthy statisticians and mathematicians working today.
Probability Approximations And Beyond
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Author : Andrew Barbour
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-12-07
Probability Approximations And Beyond written by Andrew Barbour and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-07 with Mathematics categories.
In June 2010, a conference, Probability Approximations and Beyond, was held at the National University of Singapore (NUS), in honor of pioneering mathematician Louis Chen. Chen made the first of several seminal contributions to the theory and application of Stein’s method. One of his most important contributions has been to turn Stein’s concentration inequality idea into an effective tool for providing error bounds for the normal approximation in many settings, and in particular for sums of random variables exhibiting only local dependence. This conference attracted a large audience that came to pay homage to Chen and to hear presentations by colleagues who have worked with him in special ways over the past 40+ years. The papers in this volume attest to how Louis Chen’s cutting-edge ideas influenced and continue to influence such areas as molecular biology and computer science. He has developed applications of his work on Poisson approximation to problems of signal detection in computational biology. The original papers contained in this book provide historical context for Chen’s work alongside commentary on some of his major contributions by noteworthy statisticians and mathematicians working today.
Beyond Chance And Credence
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Author : Wayne C. Myrvold
language : en
Publisher: Oxford University Press
Release Date : 2021-02-11
Beyond Chance And Credence written by Wayne C. Myrvold and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-11 with Philosophy categories.
Concepts related to probability permeate physics. This is most obvious in statistical mechanics, in which probabilities appear explicitly, but even in cases when predictions are made with near-certainty, there are implicit probabilistic assumptions in play. How are we to understand these probabilistic concepts? How do they apply to the physical world? Beyond Chance and Credence offers a fresh look at these familiar topics, urging readers to see them in a new light. The book provides an overview of the history of philosophical debates about the nature of probability over the last three centuries, and clear and accessible introductions to conceptual issues in probability theory, thermodynamics, and statistical mechanics. Myrvold argues that the traditional choice between probabilities as objective chances or else as degrees of belief is too limiting, and introduces a new concept, epistemic chances, that combines physical and epistemic considerations. He goes on to show that conceiving of probabilities in this way solves some of the puzzles associated with the use of probability and statistical mechanics. The result is an innovative perspective on one of the most central topics in the philosophy of science.
Information Theoretic Methods For Estimating Of Complicated Probability Distributions
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Author : Zhi Zong
language : en
Publisher: Elsevier
Release Date : 2006-08-15
Information Theoretic Methods For Estimating Of Complicated Probability Distributions written by Zhi Zong and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-15 with Mathematics categories.
Mixing up various disciplines frequently produces something that are profound and far-reaching. Cybernetics is such an often-quoted example. Mix of information theory, statistics and computing technology proves to be very useful, which leads to the recent development of information-theory based methods for estimating complicated probability distributions. Estimating probability distribution of a random variable is the fundamental task for quite some fields besides statistics, such as reliability, probabilistic risk analysis (PSA), machine learning, pattern recognization, image processing, neural networks and quality control. Simple distribution forms such as Gaussian, exponential or Weibull distributions are often employed to represent the distributions of the random variables under consideration, as we are taught in universities. In engineering, physical and social science applications, however, the distributions of many random variables or random vectors are so complicated that they do not fit the simple distribution forms at al. Exact estimation of the probability distribution of a random variable is very important. Take stock market prediction for example. Gaussian distribution is often used to model the fluctuations of stock prices. If such fluctuations are not normally distributed, and we use the normal distribution to represent them, how could we expect our prediction of stock market is correct? Another case well exemplifying the necessity of exact estimation of probability distributions is reliability engineering. Failure of exact estimation of the probability distributions under consideration may lead to disastrous designs. There have been constant efforts to find appropriate methods to determine complicated distributions based on random samples, but this topic has never been systematically discussed in detail in a book or monograph. The present book is intended to fill the gap and documents the latest research in this subject. Determining a complicated distribution is not simply a multiple of the workload we use to determine a simple distribution, but it turns out to be a much harder task. Two important mathematical tools, function approximation and information theory, that are beyond traditional mathematical statistics, are often used. Several methods constructed based on the two mathematical tools for distribution estimation are detailed in this book. These methods have been applied by the author for several years to many cases. They are superior in the following senses: (1) No prior information of the distribution form to be determined is necessary. It can be determined automatically from the sample; (2) The sample size may be large or small; (3) They are particularly suitable for computers. It is the rapid development of computing technology that makes it possible for fast estimation of complicated distributions. The methods provided herein well demonstrate the significant cross influences between information theory and statistics, and showcase the fallacies of traditional statistics that, however, can be overcome by information theory. Key Features: - Density functions automatically determined from samples - Free of assuming density forms - Computation-effective methods suitable for PC - density functions automatically determined from samples - Free of assuming density forms - Computation-effective methods suitable for PC
Probability Approximations For Sums Of Independent And Non Identically Distributed Random Variables
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Author : S. Vasudevan
language : en
Publisher:
Release Date : 1981
Probability Approximations For Sums Of Independent And Non Identically Distributed Random Variables written by S. Vasudevan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with categories.
Neural Networks For Conditional Probability Estimation
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Author : Dirk Husmeier
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Neural Networks For Conditional Probability Estimation written by Dirk Husmeier and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
Conventional applications of neural networks usually predict a single value as a function of given inputs. In forecasting, for example, a standard objective is to predict the future value of some entity of interest on the basis of a time series of past measurements or observations. Typical training schemes aim to minimise the sum of squared deviations between predicted and actual values (the 'targets'), by which, ideally, the network learns the conditional mean of the target given the input. If the underlying conditional distribution is Gaus sian or at least unimodal, this may be a satisfactory approach. However, for a multimodal distribution, the conditional mean does not capture the relevant features of the system, and the prediction performance will, in general, be very poor. This calls for a more powerful and sophisticated model, which can learn the whole conditional probability distribution. Chapter 1 demonstrates that even for a deterministic system and 'be nign' Gaussian observational noise, the conditional distribution of a future observation, conditional on a set of past observations, can become strongly skewed and multimodal. In Chapter 2, a general neural network structure for modelling conditional probability densities is derived, and it is shown that a universal approximator for this extended task requires at least two hidden layers. A training scheme is developed from a maximum likelihood approach in Chapter 3, and the performance ofthis method is demonstrated on three stochastic time series in chapters 4 and 5.
Moments In Probability And Approximation Theory
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Author : George A. Anastassiou
language : en
Publisher: Halsted Press
Release Date : 1993
Moments In Probability And Approximation Theory written by George A. Anastassiou and has been published by Halsted Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Approximation theory categories.
Probability Approximations Via The Poisson Clumping Heuristic
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Author : David Aldous
language : en
Publisher: Springer
Release Date : 2010-12-01
Probability Approximations Via The Poisson Clumping Heuristic written by David Aldous and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-01 with Mathematics categories.
If you place a large number of points randomly in the unit square, what is the distribution of the radius of the largest circle containing no points? Of the smallest circle containing 4 points? Why do Brownian sample paths have local maxima but not points of increase, and how nearly do they have points of increase? Given two long strings of letters drawn i. i. d. from a finite alphabet, how long is the longest consecutive (resp. non-consecutive) substring appearing in both strings? If an imaginary particle performs a simple random walk on the vertices of a high-dimensional cube, how long does it take to visit every vertex? If a particle moves under the influence of a potential field and random perturbations of velocity, how long does it take to escape from a deep potential well? If cars on a freeway move with constant speed (random from car to car), what is the longest stretch of empty road you will see during a long journey? If you take a large i. i. d. sample from a 2-dimensional rotationally-invariant distribution, what is the maximum over all half-spaces of the deviation between the empirical and true distributions? These questions cover a wide cross-section of theoretical and applied probability. The common theme is that they all deal with maxima or min ima, in some sense.
A Modern Introduction To Probability And Statistics
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Author : F.M. Dekking
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30
A Modern Introduction To Probability And Statistics written by F.M. Dekking and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-30 with Mathematics categories.
Suitable for self study Use real examples and real data sets that will be familiar to the audience Introduction to the bootstrap is included – this is a modern method missing in many other books
Stellar Atmospheres Beyond Classical Models
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Author : L. Crivellari
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Stellar Atmospheres Beyond Classical Models written by L. Crivellari and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
The theory of stellar atmospheres is one of the most important branches of modern astrophysics. It is first of all a major tool for understanding all aspects of stars. As the physical properties of their outer layers can now be found with high precision, firm conclusions can be drawn about the internal structure and evolution of stars. Moreover, improvements in our knowledge of the chemical composition of stars is shedding new light on the chemical evolution of galaxies and of the Universe as a whole. Because the outer layers of stars are among the best-understood astrophysical objects, the theory of stellar atmospheres plays an important role in the study of many other types of objects. These include planetary nebulae, H II regions, interstellar matter, and objects of interest in high-energy astrophysics, such as accretion disks (close binaries, dwarf novae, cataclysmic variables, quasars, active galactic nuclei), pulsar magnetospheres, and Seyfert galaxies. Finally, as stars provide a laboratory in which plasmas can be studied under more extreme conditions than on earth, the study of stellar atmospheres has strong connections with modern physics. Astronomical observations provided a vital stimulus in the early stages of quantum theory and atomic physics; even today topics such as low-temperature dielectronic recombination develop hand in hand with the interpretation of stellar and nebular spectra. Early work on MHD was similiarly motivated. Many such connections remain to be explored.